Answer:
Perimeter of the dog park = 15.4 yards
Step-by-step explanation:
Coordinates of the vertices of the given triangle are,
P(1, 2), Q(1, 6), R(-4, 2)
Since distance between the two points and
is,
d =
Length of PQ =
PQ = 4
Length of PR =
PR = 5
Length of QR =
QR =
=
= 6.4 yards
Therefore, perimeter of the given triangle = PQ + QR + PR
= 4 + 6.4 + 5
= 15.4 yards
Answer:
volume V of the solid
Step-by-step explanation:
The situation is depicted in the picture attached
(see picture)
First, we divide the segment [0, 5] on the X-axis into n equal parts of length 5/n each
[0, 5/n], [5/n, 2(5/n)], [2(5/n), 3(5/n)],..., [(n-1)(5/n), 5]
Now, we slice our solid into n slices.
Each slice is a quarter of cylinder 5/n thick and has a radius of
-k(5/n) + 5 for each k = 1,2,..., n (see picture)
So the volume of each slice is
for k=1,2,..., n
We then add up the volumes of all these slices
Notice that the last term of the sum vanishes. After making up the expression a little, we get
But
we also know that
and
so we have, after replacing and simplifying, the sum of the slices equals
Now we take the limit when n tends to infinite (the slices get thinner and thinner)
and the volume V of our solid is
